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The small sample imbalance (S&I) problem is a major challenge in machine learning and data analysis. It is characterized by a small number of samples and an imbalanced class distribution, which leads to poor model performance. In addition,…

Machine learning models often encounter samples that are diverged from the training distribution. Failure to recognize an out-of-distribution (OOD) sample, and consequently assign that sample to an in-class label significantly compromises…

The increasing use of deep learning across various domains highlights the importance of understanding the decision-making processes of these black-box models. Recent research focusing on the decision boundaries of deep classifiers, relies…

In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population…

Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical…

We consider a reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$, and the…

Neural networks are often utilised in critical domain applications (e.g. self-driving cars, financial markets, and aerospace engineering), even though they exhibit overconfident predictions for ambiguous inputs. This deficiency demonstrates…

In this paper the problem of {\em learning} appropriate domain-specific bias is addressed. It is shown that this can be achieved by learning many related tasks from the same domain, and a theorem is given bounding the number tasks that must…

For measuring the strength of visually-observed subpopulation differences, the Population Difference Criterion is proposed to assess the statistical significance of visually observed subpopulation differences. It addresses the following…

Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…

This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…

Estimating the generalization performance is practically challenging on out-of-distribution (OOD) data without ground-truth labels. While previous methods emphasize the connection between distribution difference and OOD accuracy, we show…

We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered.…

Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models…

The increased success of Deep Learning (DL) has recently sparked large-scale deployment of DL models in many diverse industry segments. Yet, a crucial weakness of supervised model is the inherent difficulty in handling out-of-distribution…

Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other one…

In classification problems, the purpose of feature selection is to identify a small, highly discriminative subset of the original feature set. In many applications, the dataset may have thousands of features and only a few dozens of samples…

Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…

Label distribution learning (LDL) differs from multi-label learning which aims at representing the polysemy of instances by transforming single-label values into descriptive degrees. Unfortunately, the feature space of the label…

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has…